Question 1

Which of the following relations is NOT a function?

Accepted Answer

$$\{(1,2), (1,3), (2,4), (3,5)\}$$

Question 2

Given the relation $$\{(4,3), (4,7), (7,3), (7,7)\}$$, what is the domain and range?

Accepted Answer

Domain: $$\{4,7\}$$, Range: $$\{3,7\}$$

Question 3

Which equation defines $$y as a $$function of $$x$$?

Accepted Answer

$$x + y = 49$$

Question 4

Evaluate $$f(x) = 6x + 7 at$$ $$x = 3$$ and $$x = -3. $$What is the sum $$f(3) + f(-3)$$?

Accepted Answer

$$25 + (-11) = 14$$

Question 5

Given $$f(x) = x^2$ + 3x + 2$$, what is $$f(x+4)$$?

Accepted Answer

$$(x+4)^2 + 3(x+4) + 2$

Question 6

A function $$f(x) is $$graphed and passes the vertical line test. Which statement is true?

Accepted Answer

The graph represents a function because each $$x$$ value corresponds to exactly one $$y$$ value.

Question 7

Given $$f(x) = \frac{6x^2$ - 1}{x^2$}$$, what is $$f(-x)$$?

Accepted Answer

$$\frac{6x^2$ - 1}{x^2$}$$

Question 8

A bar graph shows the wage gap between men and women from 1980 to 2010. The function $$G(x) = -0.01x^2$ + x + 55$$ models the wage gap, where $$x is $$years after 1980. What does $$G(30)$$ represent?

Accepted Answer

$$G(30)$$ represents a wage gap of $$76\% in $$the year $$2010.$$

Question 9

If a function $$f$$ has domain $$[0, \infty)$$ and range $$(-\infty, -2]$$, which of the following could be the $$y-$$intercept?

Accepted Answer

$$-2$$

Question 10

Given the function $$f(x) = x^2$ + 3x + 2$$, what is $$f(-x)$$?

Accepted Answer

$$x^2 - 3x + 2$

Question 11

A function $$g is $$graphed and $$g(-8) = 9. $$Which point represents this information?

Accepted Answer

$$(-8, 9)$$

Question 12

If $$f(x)$$ has domain $$(-\infty, \infty)$$ and range $$(-\infty, 1]$$, what is the largest possible value of $$f(x)$$?

Accepted Answer

$$1$$

Question 13

Which of the following statements about the vertical line test is correct?

Accepted Answer

If any vertical line crosses the graph more than once, the relation is not a function.

Question 14

Given $$f(x) = 6x + 7$$, what is $$f(x+4)$$?

Accepted Answer

$$6x + 31$$

Question 15

If $$f(x) = \frac{6x^2$ - 1}{x^2$}$$, what is $$f(3)$$?

Accepted Answer

$$\frac{53}{9}$$

Question 16

A function $$f$$ has domain $$(-\infty, \infty)$$ and range $$(-\infty, 0). $$Which of the following is true about its $$x-$$intercepts?

Accepted Answer

There are no $$x-$$intercepts.

Question 17

If $$f(x) is $$graphed and $$f(1) = 0$$, what does this mean?

Accepted Answer

The graph passes through the point $$(1,0).$$

Question 18

Given the function $$G(x) = -0.01x^2$ + x + 55$$ modeling the wage gap, if the actual wage gap in 2010 is $$81\%$$ and $$G(30) = 76$$, does the function overestimate or underestimate the actual data, and by how much?

Accepted Answer

The function underestimates by $$5\%.$$

Question 19

If a function $$f$$ has domain $$[0, \infty)$$ and range $$(-\infty, -2]$$, which of the following could be the $$x-$$intercept?

Accepted Answer

There is no $$x-$$intercept.

College Algebra: Basics of Functions and Graphs – Step-by-Step Study Guidance

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